A.Z.
When one sac is empty and has stopped growing it is called a blighted ovum. Often with a twin pregnancy it is also called a vanishing twin syndrome or a blighted twin if it occurs in the first trimester.
This should not cause any problems with the surviving twin and it will be treated like any other single pregnancy you have had as the twin loss happened in the very early stages of pregnancy. It might cause a problem if you lost a twin in the second or third trimester.
The empty sac will either be absorbed into your body, absorbed by the surviving twin, or you might experience some mild bleeding to pass the remains. However, if you do have any bleeding and/or cramping you still want to alert your OB and have it checked out to make sure there isn't a problem with the remaining twin.
I'm sorry for your loss but want to offer congrats on your pregnancy with the surviving twin.